We show that the plastic deformation of snow under uniaxial compression is characterized by complex spatio-temporal strain localization phenomena. Deformation is characterized by repeated nucleation and propagation of compaction bands. Compaction bands are also observed during the very first stage of compression of solid foams where a single band moves across the sample at approximately constant stress. However, snow differs from these materials as repeated nucleation and propagation of bands occurs throughout the subsequent hardening stage until the end of the deformation experiment. Band nucleation and/or reflection of bands at the sample boundaries are accompanied by stress drops which punctuate the stress strain curve. A constitutive model is proposed which quantitatively reproduces all features of this oscillatory deformation mode. To this end, a well-established compressive plasticity framework for solid foams is generalized to account for shear softening behavior, time dependence of microstructure ('rapid sintering') and non-locality of damage processes in snow. arXiv:1501.02184v1 [cond-mat.soft]

Cellular solids usually possess random microstructures that may contain a characteristic length scale, such as the cell size. This gives rise to size dependent mechanical properties where large systems behave differently from small systems. Furthermore, these structures are often irregular, which not only affects the size dependent behavior but also leads to significant property variations among different microstructure realizations. The computational model for cellular microstructures is based on networks of Timoshenko beams. It is a computationally efficient approach allowing to obtain statistically representative averages from computing large numbers of realizations. For detailed analysis of the underlying deformation mechanisms an energetically consistent continuization method was developed which links the forces and displacements of discrete beam networks to equivalent spatially continuous stress and strain fields. This method is not only useful for evaluation and visualization purposes but also allows to perform ensemble averages of, e.g., continuous stress patterns -an analysis approach which is highly beneficial for comparisons and statistical analysis of microstructures with respect to different degrees of structural disorder. (Stefan Liebenstein ) 1 In the following, we denote by 'microstructure' internal sub-structures of a material which are characterized by length scales well below the size of a specimen or device, the geometry of which defines the 'macrostructure'.

We present results of a two-scale model of disordered cellular materials where we describe the microstructure in an idealized manner using a beam network model and then make a transition to a Cosserat-type continuum model describing the same material on the macroscopic scale. In such scale transitions, normally either bottom-up homogenization approaches or top-down reverse modelling strategies are used in order to match the macro-scale Cosserat continuum to the micro-scale beam network. Here we use a different approach that is based on an energetically consistent continuization scheme that uses data from the beam network model in order to determine continuous stress and strain variables in a set of control volumes defined on the scale of the individual microstructure elements (cells) in such a manner that they form a continuous tessellation of the material domain. Stresses and strains are determined independently in all control volumes, and constitutive parameters are obtained from the ensemble of control volume data using a least-square error criterion. We show that this approach yields material parameters that are for regular honeycomb structures in close agreement with analytical results. For strongly disordered cellular structures, the thus parametrized Cosserat continuum produces results that reproduce the behavior of the micro-scale beam models both in view of the observed strain patterns and in view of the macroscopic response, including its size dependence.

A higher order continuum model is presented, which is able to capture size effects and regularize softening in rotational, shearing and especially compressive settings. It is shown that with a minimal setting of 3 additional constitutive parameters the model has all desired properties. For parameter identification an example system of a honeycomb structure is investigated.